Passive earth pressure for sloped deflection berm 1

[icupat11]

Hi,
I hope the image attached to this.
I am considering a deflection wall (for a mud flow/debris flow) that has a cheap/light sheetpile in front of an earth berm (assume it has minimal resistance to impact force shown as a car for illustration only). My proposed design is the lower image where there is some crest width "x" and then it goes down at 2h:1v to original ground.

My question - how the heck do I calculate the Kp (passive pressure) for this odd shape which is definitely not "infinite length" backfill and is less than 45 + phi/2 (eg. the rupture/failure plane)- so is for sure not the "standard" Kp you'd calculated.

NAVFAC has a chart that gives you the reduction for a negatively sloped backfill IF it starts at the edge of pile.. I've show the result in the image.. for 30 degrees and dense sand (phi = 39) goes from Kp= 4.4 to 1.4.. makes sense... but in my design case we will have a 3 m wide crest width flat behind the pile - so a better scenario and closer to the "infinite length flat backfill" case.

I guess is there an alternative method of just getting the passive force available - without actually needing to calculate Kp specifically - other than using a finite element program?

Of note mud flows travel at 5 to 10 m/s and impact forces are at 100 to 300 kPa, so there is significant force...
In my research people seem to just "build it" for pure earthfill deflection berms and don't do a sliding calc or passive resistance calce.. I would think in transporation/traffic design and crash walls this is considered - but maybe they just use reinforced concrete, rather than earthfill passive pressure.

Any thoughts would be appreciated.

 

[EireChch]

Culman graphical method

 

[icupat11]

Is there an excel or program out there which can do culman easily?

 

[EireChch]

No, it’s easy. Find a text book. It’s just areas and unit weights!

 

[CaGeotech]

Hi,
The way I would handle this is by using a program like Slope/W or Slide to model the berm and estimate the passive pressure. My colleague has a nice example on his website.

Link

 

[icupat11]

thanks all and especially CaGeotech. the slopeW and slide method makes sense to me and can deal with any geometry.. perfect.. though multi-layer gets a bit tedious.. luckily i'm looking at one layer.